Answer:
Solve by factoring.
1. 2x^2+9x+26=-4x+5
2x²+9x+4x+26-5=0
2x²+13x+21=0
doing middle term factorization
2x²+7x+6x+21=0
x(2x+7)+3(2x+7)=0
<u>(</u><u>2</u><u>x</u><u>+</u><u>7</u><u>)</u><u>(</u><u>x</u><u>+</u><u>3</u><u>)</u><u>=</u><u>0</u>
<u>either</u>
<u>x</u><u>=</u><u>-</u><u>7</u><u>/</u><u>2</u>
<u>or</u>
<u>x</u><u>=</u><u>-</u><u>3</u><u>.</u>
2.
3x^2-6x-4=0
comparing above equation with ax²+bx+c=0
we get
a=3
b=-6
c=-4
By using quadratic equation
x=![\frac{ - b±\sqrt{ {b}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%20b%C2%B1%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20)
Substituting value
x=![\frac{ 6±\sqrt{ {-6}^{2} - 4*3*-4 }}{2*-4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B1%5Csqrt%7B%20%7B-6%7D%5E%7B2%7D%20-%204%2A3%2A-4%20%7D%7D%7B2%2A-4%7D%20)
x=![\frac{ 6±\sqrt{ {84}}}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B1%5Csqrt%7B%20%7B84%7D%7D%7D%7B-8%7D%20)
x=![\frac{ 6±2\sqrt{ {21}}}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B12%5Csqrt%7B%20%7B21%7D%7D%7D%7B-8%7D%20)
-8x=6±2√21
taking positive
-8x=6+2√21
x=![\frac{6+2√21}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%2B2%E2%88%9A21%7D%7B-8%7D%20)
x=-![\frac{3+√21}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%2B%E2%88%9A21%7D%7B4%7D%20)
taking negative
-8x=6-2√21
x=![\frac{6-2√21}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6-2%E2%88%9A21%7D%7B-8%7D%20)
x=-![\frac{3-√21}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3-%E2%88%9A21%7D%7B4%7D%20)
Answer:
x = 6
Step-by-step explanation:
Here, we want to solve for the value of x
mathematically, tangents drawn from the same point to touch two points on a circle, are the same distance from the external point
thus;
QR = RS
Thus;
3x + 8 = 26
3x = 26-8
3x = 18
x = 18/3
x = 6
Answer:
ρ = 35% or 0.35
ρ with ^ =
or equivalently 46%
Step-by-step explanation:
ρ represents the population proportion of the bus riders, with a monthly pass, who are students.
The population proportion is simply the percentage of the entire population with a particular characteristic. We have been informed that in a city, 35% of the bus riders with a monthly pass are students. This means that 35% of the whole population of bus riders with a monthly pass are students. Therefore, our ρ is simply 35% or 0.35.
ρ with ^ represents the sample proportion of the bus riders, with a monthly pass, who are students. This is a statistic or an estimator as it is normally used to estimate the value of ρ, the population proportion. It is calculated using the formula;
ρ with ^ = ![\frac{x}{n}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bn%7D)
where n represents the size of the sample and x the number of individuals in the sample with a certain desired characteristic. We have been informed that;
in a random sample of 50 bus riders with monthly passes, 23 are students.
Using the above formula and the values given we have;
ρ with ^ =
or equivalently 46%